Profile consistency

Profile consistency (or profile resilience or stiffness) is the observation that profiles (of temperature, density, and pressure) often tend to adopt roughly the same shape (in tokamaks), regardless of the applied heating and fueling profiles. The resulting (stiff) profiles are known as canonical profiles. This phenomenology is due to plasma self-organisation, i.e., the feedback mechanism regulating the profiles (by turbulence) is often dominant over the various source terms.

Observations (tokamaks)

• TFTR
• ASDEX
• Various devices

Observations (stellarators)

• W7-AS
• Various devices

Quantification methods

It is customary to introduce an ad-hoc transport model with a critical gradient (sharply enhanced transport above a critical value of the local gradient) to attempt to quantify the 'criticality' of transport:

$\chi =\chi _{0}+\chi _{1}\xi \left({\frac {R}{L_{T}}}-{\frac {R}{L_{T,crit}}}\right)^{\alpha }H_{c}$

Here, H_c is a step function (to activate supercritical transport), L_T = T/∇ T is the temperature gradient scale length, and χ is the heat transport coefficient (χ₀ and χ₁ being the sub- and super-critical transport coefficients, and ξ the 'stiffness factor'). This sharply non-linear dependence of the transport coefficient on the relevant profile parameter (L_T) makes the profiles 'stiff' in the sense that the gradients (L_T) will change little in response to a large change in drive (the heat source) in the appropriate parameter range.

However, it is possible to devise methods for the objective quantification of profile stiffness that do not depend so much on the introduction of any ad-hoc model, simply by making this idea of stiffness explicit (i.e., by measuring the response of the gradient to a change in drive or heat source).